Power-Aware Routing and Network Design with Bundled Links: Solutions and Analysis

Algorithm 2

MD-FDH.

(1) Given a source 𝑘∈𝐾, the flows 𝑓^𝑘_𝑢𝑣∀(𝑢,𝑣)∈𝐸 and the traffic

  demand 𝜏_𝑘𝑑∀(𝑘,𝑑)∈𝐷

(2) Residual topology 𝐺^𝑅(𝑉,𝐸^𝑅) and 𝐷^𝑘={𝑑: (𝑘,𝑑)∈𝐷}

(3) Initialize 𝑝𝑎𝑡ℎ_𝑐𝑜𝑢𝑛𝑡[𝑖]=0∀𝑖∈𝐷^𝑘

(4) repeat

(5)  Set 𝐸^𝑅={(𝑢,𝑣): 𝑓^𝑘_𝑢𝑣>0}∀(𝑢,𝑣)∈𝐸

(6)  Select the destination node 𝑡∶𝜏_𝑘𝑡=min_𝑑∈𝐷^𝑘{𝜏_𝑘𝑑};

(7)  Find the path 𝑃=SPR(𝐺^𝑅) from 𝑘 to 𝑡;

(8)  Compute 𝑝𝑎𝑡ℎ_𝑣𝑎𝑙𝑢𝑒[𝑡,𝑝𝑎𝑡ℎ_𝑐𝑜𝑢𝑛𝑡[𝑡]]=min_{(𝑢,𝑣)∈𝑃}{𝜏_𝑘𝑡,𝑓^𝑘_𝑢𝑣};

(9)  Update 𝜏_𝑘𝑡−=𝑝𝑎𝑡ℎ_𝑣𝑎𝑙𝑢𝑒[𝑡,𝑝𝑎𝑡ℎ_𝑐𝑜𝑢𝑛𝑡[𝑡]] and

    𝑓^𝑘_𝑢𝑣−=𝑝𝑎𝑡ℎ_𝑣𝑎𝑙𝑢𝑒[𝑡,𝑝𝑎𝑡ℎ_𝑐𝑜𝑢𝑛𝑡[𝑡]]∀(𝑢,𝑣)∈𝑃;

(10)  Set 𝑝𝑎𝑡ℎ_𝑙𝑖𝑠𝑡[𝑡,𝑝𝑎𝑡ℎ_𝑐𝑜𝑢𝑛𝑡[𝑡]]=𝑃;

(11) ++ 𝑝𝑎𝑡ℎ_𝑐𝑜𝑢𝑛𝑡[𝑡];

(12) until (𝑓^𝑘_𝑢𝑣==0  ∀(𝑢,𝑣)∈𝐸)